What is the solution set of {x | x > -5} {x | x < 5}?
A. the empty set
B. the numbers between -5 and 5
C. all numbers except -5 and 5
D. all real numbers
plot the intervals on the number line
If the solution set is {x | x > -5} AND {x | x < 5}
-5 < x < 5
If it is {x | x > -5} OR {x | x < 5}
then it is the whole number line.
To find the solution set of the given set builder notation {x | x > -5} ∩ {x | x < 5}, we need to determine the values that satisfy both conditions.
First, let's analyze the condition x > -5. This means that any value of x that is greater than -5 will satisfy this condition.
Second, let's consider the condition x < 5. This condition indicates that any value of x that is less than 5 will meet this requirement.
By combining both conditions, we can conclude that the solution set will contain the values that satisfy both conditions, which are all the numbers greater than -5 and less than 5.
Therefore, the solution set of {x | x > -5} ∩ {x | x < 5} is the interval (-5, 5). It includes all the numbers between -5 and 5 but does not include -5 and 5 themselves.
Based on the answer choices:
A. the empty set - Incorrect, as there are numbers in the solution set.
B. the numbers between -5 and 5 - Incorrect, as it does not include -5 and 5.
C. all numbers except -5 and 5 - Incorrect, as it includes numbers that are not in the solution set.
D. all real numbers - Incorrect, as the solution set is limited to the interval (-5, 5).
Therefore, the correct answer is B. the numbers between -5 and 5.
To find the solution set of the given set {x | x > -5} {x | x < 5}, we need to determine the range of values that satisfy both conditions.
The set {x | x > -5} represents all numbers that are greater than -5. This means that any number larger than -5 will satisfy this condition.
Similarly, the set {x | x < 5} represents all numbers that are less than 5. Hence, any number smaller than 5 will satisfy this condition.
To find the common set of values that satisfy both conditions, we need to find the intersection of the two sets.
Since any number larger than -5 and smaller than 5 satisfies both conditions, the solution set is the range of numbers between -5 and 5, excluding -5 and 5 themselves.
Therefore, the correct answer is C. all numbers except -5 and 5.